Details

Time bar (total: 8.4s)

sample100.0ms

Algorithm
intervals
Results
36.0ms786×body80nan
9.0ms29×body640valid
8.0ms167×body80valid
7.0ms11×body1280valid
5.0ms32×body320valid
2.0ms18×body160valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0227
1386
2536
3616
4786
51106
61756
72846
83636
93926
104766
114766

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 9.9b

Counts
2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z (log (- 1.0 y))) t)
0.0b
(* z (log (- 1.0 y)))
0.1b
(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.7b
(log (- 1.0 y))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×log-prod
24×add-sqr-sqrt
22×*-un-lft-identity
12×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in associate--l+
8×pow1
7×add-exp-log
6×add-cbrt-cube add-log-exp
5×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×associate-*l* prod-diff
2×log-div flip3-- log-pow flip--
1×sub-neg fma-neg diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 87
Calls
4 calls:
9.0ms
(- (* z (log (- 1.0 y))) t)
6.0ms
(* z (log (- 1.0 y)))
1.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.0ms
(log (- 1.0 y))

series299.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* z (log (- 1.0 y))) t)
63.0ms
(* z (log (- 1.0 y)))
128.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
48.0ms
(log (- 1.0 y))

simplify46.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0461620
11606547
25001537

prune311.0ms

Filtered
99 candidates to 77 candidates (77.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New93699
Fresh101
Picked101
Done000
Total956101

Merged error: 0.1b

Counts
101 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.1b
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
111×add-sqr-sqrt
80×times-frac
76×*-un-lft-identity
74×associate-*r*
73×add-cube-cbrt
56×unpow-prod-down
51×prod-diff
46×associate--l+
34×distribute-rgt-in distribute-lft-in
29×add-exp-log
24×unpow2 sqr-pow
21×pow1
18×unswap-sqr
13×log-pow
12×log-prod
11×prod-exp add-cbrt-cube
9×div-exp
6×pow-to-exp associate-*l* pow-exp add-log-exp
5×sub-neg
4×expm1-log1p-u log1p-expm1-u
3×associate-*r/ cbrt-unprod
2×flip3-- pow-prod-down *-commutative flip-- distribute-lft-out--
1×cbrt-undiv fma-neg diff-log fma-udef div-inv difference-of-squares
Counts
4 → 233
Calls
4 calls:
21.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
10.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
13.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
1.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series435.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
98.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
119.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
166.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify112.0ms

Algorithm
egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09363375
138932186
250012179

prune757.0ms

Filtered
245 candidates to 149 candidates (60.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2423245
Fresh145
Picked011
Done000
Total2438251

Merged error: 0.1b

Counts
251 → 8

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
0.1b
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
71×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
37×add-cube-cbrt *-un-lft-identity
26×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
8×add-cbrt-cube
6×pow-to-exp pow-exp
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×cbrt-unprod fma-udef
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv
Counts
3 → 132
Calls
3 calls:
25.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
1.0ms
(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
1.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series341.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
109.0ms
(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
178.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify66.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0616990
12555827
25002826

prune484.0ms

Filtered
141 candidates to 94 candidates (66.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1410141
Fresh066
Picked011
Done011
Total1418149

Merged error: 0.1b

Counts
149 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
12.0b
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0b
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0b
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-- pow1/3 flip--
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 80
Calls
4 calls:
7.0ms
(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
7.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
6.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
413.0ms
(* (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
346.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
369.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
345.0ms
(cbrt (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05932423
123002263
250012173

prune531.0ms

Filtered
92 candidates to 75 candidates (81.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New92092
Fresh055
Picked011
Done022
Total928100

Merged error: 0.1b

Counts
100 → 8

regimes194.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02212
12212

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s24631×body80nan
287.0ms5629×body80valid
266.0ms877×body640valid
214.0ms363×body1280valid
126.0ms707×body320valid
50.0ms462×body160valid